题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153304-64422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153305-12190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153305-33949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153305-33949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153305-12190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153305-33949.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153305-28510.png)
解析
试题分析:条件中给出一个直线系,需要先求出直线所过的定点,根据定点是椭圆的焦点,及椭圆C上的点到点F的最大距离为8,写出椭圆中三个字母系数要满足的条件,解方程组得到结果,写出椭圆的方程解:由(1+4k)x-(2-3k)y-(3+12k)=0得(x-2y-3)+k(4x+3y-12)=0,由x-2y-3=0,4x+3y-12=0,解得F(3,0).设椭圆C的标准方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153305-33361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153306-50201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153305-28510.png)
点评:本题考查直线与圆锥曲线之间的关系,题目中首先求椭圆的方程,这是这类题目常用的一种形式,属于基础题.
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153249-63892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153250-19211.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153251-91769.png)
(1)若点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153250-21504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153252-47215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153250-33229.png)
(2)记△
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153252-42428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153252-69697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153252-56371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153253-79363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153253-26497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153250-33229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153253-12915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153238-68206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153238-90469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153239-74693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153239-84410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153239-96112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153239-86918.png)
向量
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153239-99192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153240-95275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153240-50816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153240-98737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153240-87139.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153238-68206.png)
(2)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153240-95275.png)
(3)记椭圆在直线
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153240-95275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153240-98737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153241-12035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153241-74722.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153241-12035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153241-94414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153230-69066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153230-14419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153230-48455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153230-14419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153226-93234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153227-10927.png)
A.相同的长轴长 | B.相同的焦点 |
C.相同的离心率 | D.相同的顶点 |
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153214-39054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153214-75362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153214-12439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153214-59259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153215-57122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153215-63913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153215-23153.png)
(Ⅰ)求椭圆的方程;
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153215-86058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153215-93007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153216-52939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153216-70715.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153215-86058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153216-45115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153216-17099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153216-25456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153217-18725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153217-22157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153217-13320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153217-11989.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023153218-53805.png)
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